Look at the base of the word radical - the same as the math 'radical'. A radical _should be_ someone whose ideas are outside the main stream of thought - at the edges, as a radius of a circle is the distance from the edge to the center.
I don't think it necessarily means revolutionary, although many people are both radical and revolutionary.
The opposite of radical would have to be centrist, since if you go to the opposite side of the circle, you're still on the radius.
Now, what it SHOULD mean, and how we use it, that's different. When I was younger, radical ALWAYS meant politically left, and the opposite was reactionary. But I think that's wrong. So really, we should probably almost always use it as an adjective or adverb - radical environmentalist, radically progressive. radically reactionary would actually make sense!